The Priority shipping type is a flat rate with USPS.
the shipping is calculated as a flat rate based on the origin and destination zip code. There are weight ranges that effect the shipping rate, for example 0 - 12 lbs is one rate, 13 -24 pounds is another rate.
You can use the following page to gauge what the shipping will be:
make sure to select Package and look at the Priority Mail Large Flat-Rate Box charge on the results page.